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By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By H. L. B. Gould, Jr. Wenny D. H.

TO date there has been but limited interest in alloys of 80 to 95 pct Co and Fe with or without other additions. In 1932, S. R. Williams' reported practically zero magnetostriction for the 90 pct Co-10 pct Fe alloy. This same composition was used for pole pieces to control the magnetic field in magnetrons operating at high temperatures.' In 1947, a 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn composition was investigated3 for use in ballast lamps because of its high temperature coefficient of resistance. Recently, as part of a survey of ductile and malleable magnetic alloys capable of being processed to thin gages for possible applications in memory devices, the high Co-Fe alloys have been re-examined to determine their fabricating and magnetic characteristics. Alloys from 80 up to 95 pct Co and Fe with and without additions such as vanadium were prepared. In general these all had excellent ductility and malleability. Wire was drawn to thin gages without difficulty and fine hard-drawn wires flattened to 2) The phenomenon may have potential in estimating the carbon content of molybdenum. A given solution-treating temperature and cooling rate could perhaps be calibrated so that the area fraction of surface covered by carbide could be interpreted in terms of carbon concentration. By segregating to the surface, a big "magnification" of the carbon content is obtained, which should make the method cheap, direct, and sensitive and, therefore, perhaps of interest to the molybdenum industry. This work was conducted at Battelle Memorial Institute. Financial support by the Aeronautical Systems Division, United States Air Force, under Contract No. AF 33(657)-7376, is gratefully acknowledged, and the writer is thankful for the experimental assistance of Miss Marjorie Cantin. ribbon without splitting. Similarly, strip was cold-rolled as much as 99.75 pct reduction to a 0.25 mil thickness without intermediate anneals. Samples of round and flat wire and foil, in the severely cold-worked and annealed states, were checked for magnetic characteristics. The alloys exhibited widely divergent magnetic characteristics depending on the processing and heat-treating procedures used in preparing the samples. Direct-current hysteresis loops showing the different magnetic characteristics of 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn alloys are shown in Figs. 1 to 8 inclusive, while Figs. 9 and 10 show the loops for an alloy of 82 pct Co, 11.75 pct Fe, 5.6 pct V, and 0.65 pct Mn. Figs. 1 and 2 show the high remanence and exceedingly square-loop characteristics of the hard-drawn wire and ribbon roll flattened therefrom. With the change in processing from roll flattening to flattening by drawing through flat diamond dies the resultant change in texture is accompanied by the drastic change in the shape of the loop as shown in Fig. 3. This skewed loop on annealing reverts to a more normal loop as shown in Fig. 8. The most unique loops are obtained with flat rolled strip. These are shown in Figs. 4 and 5. In the case of the hard-rolled material, Fig. 4, there is little change in induction until the magnetizing force reaches 50 oe. From 50 to 60 oe there is a sharp increase in induction to over 15,000 gauss, which for all practical purposes is saturation. The induction remains at a constant value while the magnetizing force decreases to 40 oe. At this point the

Jan 1, 1965

By E. S. Lenker, H. J. Van Hook

A complete swies of solid solutions has been found between the compounds InAs and GaAs Below the solidus. The melting relations determined by differential thermal and static quenching technzques, indicate that the liquidus and solidus are of the simple ascendant type. No evidence of unmixing of the homogeneous solid solutions was observed at sub-solidus temperatures. A quenching method for locnting the solidus, using X-ray diffraction techniques, is described in some detail. THE semi-conducting properties of compounds formed by various combinations of the less familiar intermetallic elements have created an increasing interest in the phase relations in systems involving these elements. The complete phase diagram of such a system, containing a compound of special interest, will often provide information as to the most favorable conditions for preparing large crystals from a melt, as well as specifying the temperature stability of the crystalline phase or phases produced. In view of the current importance of gallium arsenide in semiconductor research and of the structural similarities of indium arsenide, it was thought that the complete phase relations of the system InAs-GaAs should be investigated. Previous work on the system Ga-As by Koster and homa' and on In-As by Liu and peretti2 has shown that GaAs and InAs are the only compounds formed, having melting points of 1238° and 942°C, respectively. In a survey of various systems of elements from groups IIIb and Vb, spengler3 also re- Mines Ltd., for his continuing encouragement and for permission to publish the results of this work. ports complete miscibility of gallium, indium, and arsenic in the liquid state. In a partial investigation of the InAs-GaAs system, Woolley and smith4 found extensive solid solution throughout the alloy range. Their subsolidus work, however, was inconclusive at temperatures below 900" and they did not determine the liquidus relationships of the system. PRESENT INVESTIGATION The starting materials used were high-purity gallium, indium, and arsenic. The method of preparation of the compounds follows that devised by M. Shafer and is described in detail in a paper by Shafer and eiser.' The end-member compounds, GaAs and InAs, were first prepared by reaction of the elements in the desired proportions in evacuated silica glass vials. The vials were rotated in a furnace as the temperature was slowly raised to insure rapid and complete reaction at low temperatures. Thereafter the starting materials, GaAs and InAs, were melted by heating the sealed vials to 1300" and 1000°C, respectively; the vials in this case were filled as completely as possible to keep the vapor space small and thereby minimize the loss of arsenic to the vapor phase. Ten binary mixtures of these compounds were then prepared by reaction of the powdered material in the solid state just below solidus temperatures. At 900C preparations containing 3, 5, 8, 10, 25, 35, 50, and 75 mol pct GaAs were found to be single homogeneous phases, indicating a complete series of solid solutions between GaAs and InAs. Moreover, it was discovered that the homogeneity of any crystalline binary preparation could be very accurately checked by X-ray diffraction because of the large differences in unit cell dimensions of the end membe5s. The cubic lattice constant ofor GaAs is a = 5.652A and that of InAs is a = 6.061A

Jan 1, 1963

By James A. Lewis

It is the purpose of this paper to show the importance of sand characteristics, when combined with other physical data, in evaluating production obtained by secondary recovery operations, and to indicate the benefits to be gained from the application of these principles to primary production. Introduction During the past 10 years there has been a growing interest within the industry regarding the movement of fluids through oil reservoirs. A number of research projects have been directed toward the development of the physical laws governing this movement. In the period 1933 to the present, correlations between laboratory analysis of cores, reservoir fluids and well performance have been established and have been applied to successful secondary water-flooding recovery operations; and to the completion, production, reconditioning and evaluation of wells in new fields. The application of these data to water-flooding, either natural or artificial, is comparatively new, but the principlcs involved were set forth in 1880 by John F. Carll,1 who said: The flooding of an oil district is generally viewed as a great calamity, yet it may be questioned whether a larger amount of oil cannot be drawn from the rocks in that way than by any other, for it is certain that all the oil can-not be drawn from the reservoir without admission of something to take its place. If one company owned all of the wells drawing upon a pool, and had accurate records of the depth and characteristics of the oil producing stratum in each well, it is quite possible that some system might be devised by which water could be let down through certain shafts, and thus the rocks be completely voided of oil and left full of water. As it is, however, no systematized plan of action can be adopted. The careless handling of one well. by which water is let down to the oil rock, may spoil several others belonging to different parties. A clashing of interests at once arises and is likely to result in disaster to the whole district. In judging of the probable effects of the intro-duction of water into any particular oil district several things are to be considered. (1st) The time of flooding—whether early in the progress of development, while yet a large percentage of oil remains unexhausted or at a later period after the supply has suffered from long continued depletion. (2nd) The structure of the rock—whether regular and homogeneous throughout, or composed of fine sand inter. bedding connected and irregular layers of gravel, sometimes lying near the top and at others near the bottom. (3rd) The shape of the area being flooded. (4th) The position of the point at which water is admitted. in relation to the location of the surrounding wells still pumping oil. (5th) The height (which governs the pressure) of the column of water obtaining admittance. (6th) The duration of the water supply. Although we may take exception to part of Carll's reasoning, particularly " and thus the rocks be completely voided of oil and left full of water," we must give him credit for pointing out the increased effectiveness of water encroachment in displacing oil from a sand and for his recording six of the present seven considerations necessary for evaluation of production of oil by water

Jan 1, 1942

By G. W. Nabor, H. J. Ramey

A blotter-type electrolytic model was utilized to prepare flow diagrams for a field test of the in-situ combustion process. It is pointed out that the areal sweep of a combustion pattern is similar to sweep patterns that would be developed at an infinite mobility ratio, which exists (approximately) across a combustion front because of the complete removal of liquids from the sand behind it. The precision of the blotter method was tested by comparison with results obtained by other techniques and was found to be satisfactory. The blotter-type model will not furnish as much information as more elaborate and expensive potentiometric models, but its speed of operation and ease of construction make it a highly satisfactory tool to determine areal sweep patterns. A tabulation of sweep efficiency and mobility ratio is furnished for various well geometries. INTRODUCTION In connection with the first field experiment with the in-situ combustion method of oil recovery," flow diagrams for the unique well geometry and boundary conditions involved in the subject test were developed. From these diagrams, information concerning the areal sweep and distribution of flow was obtained. A survev of the literature on potentiometric models, utilized to solve two-dimensional flow problems,1,2,3,4,5,6,8,9,10 indicated that the information desired could be obtained by means of a blotter-type model by making certain modifications in the technique. The following discussion describes the application of the modified blotter-type electrolytic model to the solution of the problem of the flow of gases in an oil reservoir for an engineering appraisal of the progress of the combustion front during the first field experiment. Considerable information has been published on the theoretical aspects of electrical model techniques. One author stated that:' "The models are based on the observation that since the velocity of an ion in an electrolytic system is proportional to the potential gradient, just as the velocity of a fluid particle in a porous medium is proportional to the pressure gradient, the paths of the ions in the electrolytic systems must be similar to those of the fluid particles in a porous medium with the same geometry and equivalent boundary conditions." This suggestion of a real analogy has been established repeatedly by comparisons of analytic derivations with model results. The analogy between the movement of a combustion front and the model results is not as apparent, since the combustion process differs from water flooding and gas cycling in that the velocity of the burning front is different from the velocity of the injected fluid at the front in combustion. Analogy between electric current flow and movement of the burning front exists because the local velocity of the burning front is proportional to the air (mass) velocity at this point (assuming frontal temperatures are at least as high as the ignition temperature of the fuel). Most model studies fall into one of two categories: (1) electron conduction, or (2) ionic conduction models. Examples of these are models which employ as flow media either a thin metal sheet, or a porous blotter saturated with an electrolyte, respectively. Of the two, the porous blotter model, an ionic conduction model, appears to be the most adaptable to the flow problem that results when using in-situ combustion. This problem requires that the mobility of the particles in the model be controlled analogous to the mobility of gas flowing through burned sand of high permeability to gas and then through oil sand of lower permeability to gas. Although the blotter model has heretofore been

Jan 1, 1955

By James A. Lewis

It is the purpose of this paper to show the importance of sand characteristics, when combined with other physical data, in evaluating production obtained by secondary recovery operations, and to indicate the benefits to be gained from the application of these principles to primary production. Introduction During the past 10 years there has been a growing interest within the industry regarding the movement of fluids through oil reservoirs. A number of research projects have been directed toward the development of the physical laws governing this movement. In the period 1933 to the present, correlations between laboratory analysis of cores, reservoir fluids and well performance have been established and have been applied to successful secondary water-flooding recovery operations; and to the completion, production, reconditioning and evaluation of wells in new fields. The application of these data to water-flooding, either natural or artificial, is comparatively new, but the principlcs involved were set forth in 1880 by John F. Carll,1 who said: The flooding of an oil district is generally viewed as a great calamity, yet it may be questioned whether a larger amount of oil cannot be drawn from the rocks in that way than by any other, for it is certain that all the oil can-not be drawn from the reservoir without admission of something to take its place. If one company owned all of the wells drawing upon a pool, and had accurate records of the depth and characteristics of the oil producing stratum in each well, it is quite possible that some system might be devised by which water could be let down through certain shafts, and thus the rocks be completely voided of oil and left full of water. As it is, however, no systematized plan of action can be adopted. The careless handling of one well. by which water is let down to the oil rock, may spoil several others belonging to different parties. A clashing of interests at once arises and is likely to result in disaster to the whole district. In judging of the probable effects of the intro-duction of water into any particular oil district several things are to be considered. (1st) The time of flooding—whether early in the progress of development, while yet a large percentage of oil remains unexhausted or at a later period after the supply has suffered from long continued depletion. (2nd) The structure of the rock—whether regular and homogeneous throughout, or composed of fine sand inter. bedding connected and irregular layers of gravel, sometimes lying near the top and at others near the bottom. (3rd) The shape of the area being flooded. (4th) The position of the point at which water is admitted. in relation to the location of the surrounding wells still pumping oil. (5th) The height (which governs the pressure) of the column of water obtaining admittance. (6th) The duration of the water supply. Although we may take exception to part of Carll's reasoning, particularly " and thus the rocks be completely voided of oil and left full of water," we must give him credit for pointing out the increased effectiveness of water encroachment in displacing oil from a sand and for his recording six of the present seven considerations necessary for evaluation of production of oil by water

Jan 1, 1942

By John R. Caldon

INTRODUCTION Leasing has become a major industry in many countries because of the advantages it affords. Whilst the accounting, legal and tax treatment of leasing varies from country to country, there is far more similarity than difference. The general approach to the subject is largely the same. This paper looks to the basic financial considerations in the decision to lease or buy. TYPES OF LEASES Before embarking upon the subject, it would seem appropriate to define a "lease". A lease may be defined as: "an agreement granting one party the right to use, for a specified period of time, property owned by another party in return for a series of payments of rental by the user to the owner''. Ownership, of course, generally entitles the owner to unrestricted use of the asset over its useful life in contrast to a lease which gives the lessee use over a limited period. The distinction between the status of owner and a lessee often is fairly small. In this case we are dealing with what is generally termed a "finance lease". A finance lease is one which substantially transfers the risks and benefits of ownership from the legal owner to the lessee. For example, a finance lease would exist where the lessee enters into a lease of an asset for most of its useful life and has an option to buy the asset at the end of the lease for a price which takes cognisance of the rentals already paid. Where a lease does not substantially transfer the benefits and risks of ownership to the lessee, i.e. those benefits and risks remain with the owner and lessor, the lease is termed an "operating lease" and is an agreement for the renting and usage by the lessee of an asset owned by the lessor for a limited period. An example of an operating lease might be where a tenant leases a building for a defined period say 6 years with the rent and occupancy subject to renegotiation at the end of the lease term. The economic consequences of the distinction between a finance and an operating lease is very important. With a finance lease, the lessee has a de facto economic interest in the asset and the alternative to a finance lease is some form of purchase; with an operating lease, the lessee does not have a basic economic interest in the asset and consequently a comparison with a purchase option involves far more than simply a funding comparison. Some of the principal differences between finance and operating leases can be summarised as follows: (a) finance leases: -the risks and benefits of ownership are substantially transferred to the lessee; -the lessor normally recovers his investment during the term of the lease; -the lessor in entering into the transaction is relying more on the creditworthiness of the lessee than the underlying value of the asset; - the lease is either non-cancellable or a large penalty will apply for unilateral cancellation by the lessee; (b) operating leases -the risks and benefits of ownership remain essentially with the lessor; -the lease rental income would not normally cover the recovery of the lessor's investment; -the lessor evaluates his risk in terms of the underlying value of the assets;

Jan 1, 1985

By M. T. Simnad, C. E. Birchenall, M. H. Davis

The transport mechanisms previously proposed in wustite and hematite have been confirmed by movement of inert markers during the growth of these phases. By similar measurements the mechanism for magnetite has been determined. The rates of growth of multilayer scales on iron, magnetite and hematite on wustite, and hematite on magnetite have been measured. All rates are found to be diffusion controlled under the conditions of the experiments. MANY studies have been made of the rate of oxidation of iron in both the low temperature, film-forming region and the high temperature scaling range. The interpretation of the results has been greatly complicated by the formation of multi-layered scales containing the various phases of iron oxides. In most cases no attempt has been made to determine the composition of the scale and its dependence on time of oxidation in a quantitative manner. However, several recent studies'" have taken this variable into account. It is generally agreed that the growth of thick scales on iron follows a parabolic rate law for the increase of total thickness. In the thin film region agreement has been claimed with parabolic equations of various forms and with logarithmic equations. The discussion here will be concerned only with the formation of scales of considerable thickness, greater than several microns, although some of the conclusions may be applicable to thin films. A brief survey will be given of the solid phases of the iron-oxygen system, the stability of wiistite in bulk and in thin films, the relative densities of iron in the metal and oxides, and the kinetics of forma- tion of oxide scales on iron. New experimental results will be introduced at several points during the discussion, and an attempt will be made to formulate a mechanistic picture consistent with these observations. The experimental techniques are described in an appendix. Iron-Oxygen System Fig. la shows the iron-oxygen phase diagram. Wüstite ("FeO"): The lowest of the oxides has a NaCl type cubic lattice formed by close-packing of the relatively large oxide ions with the smaller iron ions arranged in the interstices. The ionic radius for 0' is about 1.3 A, while Fe++ has a radius of about 0.8A and Fe"' about 0.7A. Its range of existence on the phase diagram is very wide for an ionic material of this type and does not seem to include the stoi-chiometric composition FeO. These deviations appear to be well established as vacancies on iron lattice sites by the comparison of lattice parameters and densities for a series of compositions by Jette and Foote.4 The limits of the field are disputed, but the work which seems most reliable" indicates vacancies in from 5 pct to more than 12 pct of the iron sites. In order for the crystal to be electrically neutral, there must be electron holes which correspond to the formation of trivalent iron ions equal to twice the number of vacancies. Magnetite ("Fe³O4"): Considerable disagreement also exists in the literature about the stable range of the Fe³O4 field. Some diagrams show the Fe³O4 composition to be lower in oxygen than the formula indicates, but Schenck6 gives a diagram from the

Jan 1, 1952

By T. K. Perkins, L. E. Bartlett

Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenonema This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young's moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy me generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. INTRODUCTION The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface). In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young's Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50-12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry.1 An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith6 has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1.

By C. D. Cochran, F. H. Deily, M. M. White, Victor Horner

A laboratory study of the effects of physical and easily measured rheological properties upon dynamic filtration was carried out. The purpose was to determine the factors affecting dynamic filtration and thus learn how to control this important property. The recommended procedure for determining the amount of fluid loss prescribed by API Code RP 29 "Field Procedure for Testing Drilling Fluids,"' is very useful for mud conditioning purposes, but inadequate for comparing filtration properties of different muds under dynamic conditions. Where dynamic filtration control becomes important for purposes such as logging and coring, other means of evaluating filtration properties are needed. A special device and testing technique were developed to provide reliable data on filtration characteristics of different fluids under dynamic conditions. Liquid saturated rock samples were drilled with a microbit, and the amount of connate liquid displaced by the fluid being investigated was measured. The empirical testing procedure was considered reliable. A large number of laboratory-prepared and field-mixed dritling fluids with a wide range of physical properties were studied. These properties included: (I) shape of consistency curves, (2) apparent viscosity, (3) plastic viscosity, (4) yield value, (5) density, and (6) API filter loss. Test results indicate that very little, if any, trend could be established between changes in these fluid properties and dynamic filtration. INTRODUCTION During the process of drilling, excessive loss of liquid from the mud to the formation is undesirable for many reasons. Filtration can reduce production-zone permeability, cause sloughing of formations, affect electric log curves, and render the fluid data obtained from cores unreliable. Thus, it is very important that we gain a knowledge of the factors that control filtration. It is generally agreed that in any type of filtration (static, dynamic, or combinations thereof), the mechanics of filtering depend in great part upon the composition of the fluid. Moreover, it is also true that the physical and rheological properties are influenced by the composition of the fluid. Indirectly, then, it was hypothesized that a relationship existed between dynamic filtration and physical-rheological properties, two effects of a common cause—fluid composition. This paper discusses an attempt to relate filtration-while-drilling to physical and easily measured rheological properties. It is believed that the results of this study may prove useful to others in the industry who are working on the problem of understanding filtration. The industry accepted practice for determining fluid loss from drilling mud is described in API Code RP 29. The practice is to measure the amount of filtrate that passes during a given interval of time from a quiescent drilling fluid under applied pressure through a piece of filter paper. This is primarily a test of static filtration properties. Other investigators have studied filtration under dynamic conditions. Williams5 and Pro-kop5 studied radial filtration and filter-cake buildup by circulating fluid through a porous cylinder under conditions similar to actual mud flow. Nowak,4 Krueger,3,4 and Vogel3 studied the effect of filtration upon permeability by flowing mud past the face of rock Samples. In their tests, the bit action was simulated by mechanical scrapers that kept the filter cake from building up. Ferguson and Klotz2 studied three types of filtration: static, dynamic, and beneath-the-bit. They investigated each type separately, using a model well in which bottom-hole hydraulics and mechanics were closely approximated.

Jan 1, 1958

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation's supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation's need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By J. W. Whalen

The design, operation and evaluation of an instrumental method for the determination of fluid saturation in porous materials during multiphase flow studies is described. The presence of a magnetic tracer comprising approximately 20 per cent by weight of the aqueous phase is necessary in the utilization of this method. The results of two-phase relative permeability studies on two samples of porous media are presented. The realizable accuracy of the magnetic susceptibility apparatus in fluid saturation determination is estimated to be 2 saturation per cent. The response characteristics of the instrument, together with its simplicity of operation and maintenance are sufficient to recommend its use in routine laboratory studies. INTRODUCTION The problem of fluid saturation determination in laboratory multiphase flow studies characterizing oil recovery processes is one which has been given exhaustive study. Briefly the requirements which are considered essential for a method sewing this purpose are: (1) that the measurement be made external to the porous rock sample under study with no interruption of the fluid flow pattern, (2) the saturation indication must be independent of fluid distribution in the volume scanned by the measuring device, (3) the sensing element should have a small field of definition enabling several independent measurements to be made along the length of a core sample, and (4) the properties of the fluid phases should not be too greatly influenced by required tracer substances. Several methods of saturation determination have found acceptance as meeting most of the above requirements. These include resistivity,1 X-Ray absorption,2,3,4 radiotracers,5,6,7 and neutron8 diffraction The merits of these techniques have been discussed elsewhere in detail and will not be considered here. It may, however. be pointed out that the elaborate instrumentation required by the methods mentioned above, with the exception of the resistivity method (which is undesirable from other standpoints) encourages the development of methods of saturation determination which, while meeting the requirements listed, are simple to operate and maintain. It is the purpose of this paper to describe the instrumentation and evaluation of a technique for the determination of fluid saturation which combines relative simplicity with an accuracy and applicability comparable with methods now in practice. DESCRIPTION OF THE METHOD If the magnetic susceptibility of one of the fluid phases contained within a porous material is sufficiently greater than that of the remaining phases, the fluid content of the material with respect to that phase may be determined by an induction measurement. This may be accomplished by measuring the induced voltage in the secondary of a transformer which contains the porous sample and its interstitial fluids as a portion of the magnetic flux path. Since the fluids used in multiphase flow studies involving petroleum reservoir samples possess uniformly low magnetic susceptibilities, the use of a magnetic tracer in one of the fluid phases is required. In view of the relatively high paramagnetic susceptibility of salts of the transition elements, together with their high water solubility. these compounds become logical choices as tracer materials. Cobaltous chloride, having a specific magnetic susceptibility of 17.5 x 106 cgs electromagnetic units, was used as the tracer material throughout this work, in a concentration of approximately 20 per cent by weight in the aqueous phase. MAGNETIC SUSCEPTIBILITY APPARATUS Basically, the magnetic susceptibility apparatus consists of a transformer serving as the detecting head, a

Jan 1, 1955

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation's supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation's need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By H. D. Yoo, M. R. Tek, D. L. Katz

The behavior of gas-storage reservoirs subject to water drive is investigated through analog simulation on an electronic differential analyzer. The simulation technique developed on an LM-10 computer permits the prediction of reservoir volume or pressure resulting from the movement of water in the surrounding aquifer. The method developed on the analog computer consists of setting up an appropriate transfer-function circuit and feeding the arbitrary time-varying boundary conditions as an input signal. The input may be specified as gas reservoir pressure, pore volume or the water flux. Several cases studied include an isolated gas reservoir on a limited aquifer, interference among three reservoirs adjacent to a common aquifer and the growth of gas-storage volume on an aquifer. It is concluded that the method developed on an electronic differential analyzer provides an excellent technique to simulate and investigate the behavior of gas reservoirs subject to water drive. The agreement between the reservoir performance as predicted from the simulation technique and as measured from actual field data is found to be better than the range usually encountered in predicting water-drive behavior. INTRODUCTION It is generally known that some gas-storage reservoirs are located on top of blanket sands of large extent, saturated with brine called aquifers. Because the volume of the body of water associated with aquifers is usually very large and water is compressible, the cyclic pressure variations encountered in normal storage service inevitably cause unsteady, compressible flow conditions in the adjacent aquifers. The solution to radial diffusivity equation for a limited aquifer for constant terminal conditions has been know111 since the early 1930's. The solution for the constant terminal conditions for an infinite aquifer was puhlished in 1949.2 The proldem of handling the unsteady flow of water through a porous medium with time-varying boundary conditions has been studied by many investigators through the use of graphical,3 digital4 computing techniques or on an R-C type of electrical analog called a reservoir analyzer.5 The digital computer performs a series of arithmetic calculations to superimpose the solutions of constant terminal conditions, while the R-C type of analyzer permits the simulation of the continuous medium by means of "lumped-cell" electrical resistance and capacitance elements based on finite-difference approximations. The graphical method is based on the convolution integral solution of the partial differential equalion. The purpose of the present study was to simulate the behavior of an aquifer on a general-purpose, electronic differential analyzer to obtain the influx of water or the change in pressure at the reservoir continuous1r and quickly. The use of the electronic differential analyzer was based on well known solutions for the constant terminal conditions already available in the literature.2,6-8 THEORETICAL DEVELOPMENT MODEL. The gas reservoir (R) is described in relation to an aquifer in Fig. 1. The permeability and porosity of an aquifer sand, the viscosity of the brine, and the compressibility of the brine and the formation are assumed to be constant. It further is assumed that the blanket sand is not thick enough to give appreciable vertical pressure distribution. The model in consideration is circular with radial geometry. The aquifer radius can be of limited or infinite extent. The gas-water interface is assumed to be fully segregated, and the displacement of the gas by

By D. H. Gray, G. Bergamini, I. Fatt

A method developed by soil scientists for measuring permeability anisotropy of soils has been adapted for use in studies of sandstone permeability aniso-tmpy. Studies on Berea and Bandera sandstone show that permeability of these materials decreases upon application of simulated overburden pressure. Permeability reduction of Berea and Grubb sandstone cores subjected to simulated overburden pressure is shown to be a function of the ratio of radial to axial stress. INTRODUCTION The effects of mechanical stress on reservoir rock parameters are now generally accepted as being important in reservoir engineering calculations. In several oil fields the unique behavior of the reservoir has been attributed to the influence of overburden pressure or internal fluid pressure on rock permeability or fluid content. l Although the gross effects of overburden pressure on permeability, porosity, waterflood efficiency, electrical resistance and sonic velocity have now been established,3-9 there are some very interesting, and perhaps important, details of rock behavior under stress that have not heretofore been studied. In this paper we will show that permeability anistropy of several sandstones is a function of overburden pressure. We will also show that permeability reduction of cylindrical samples of two sandstones, when subjected to mechanical stress, is a function of the ratio of radial to axial stress. Most studies of overburden pressure effects made in the past have attempted to duplicate reservoir conditions by applying hydrostatic external pressure on all surfaces of the sample. Assuming perfect elasticity, that is, no viscoelastic flow during geological time, reservoir rock in situ cannot be under hydrostatic stress as is apparent from the value of 0.25 for Poisson's ratio for most rock. In the absence of tectonic forces the horizontal stress component If there are directional permeability effects, as has been reported from field and laboratory studies, l0,11 then one would expect hydrostatic stress as used in the laboratory to give a different permeability reduction from that occurring under reservoir stress conditions. The influence of stress on directional permeability was measured by a modification of the method first described by Maasland and Kirkham for use on soil samples.12 Their method permits calculation of the permeabilities along each of the three mutually perpendicular axes of a cubic sample. The modification reported in this paper extends the method to observing these permeabilities when the sample is under hydrostatic stress. The Hassler sleeve type of core holder is satisfactory for studying overburden pressure effects on permeability if a known force is applied to the end plugs. Wyble6 used a sleeve core holder but did not load the end plugs. In this paper we combine sleeve pressure and axial force to give permeability changes which we believe are close to those occurring in reservoirs when reservoir pressure changes. The combination of sleeve pressure and axial force assumes, however, that the sleeve pressure simulates both vertical stress and horizontal stress in one direction. METHOD PERMEABILITY ANISOTROPY The Maasland and Kirkhaml2 method of measuring permeability anisotropy uses a cube of porous material which is Open On three faces and has discs with a Center hole for an air inlet cemented to the other three mutually perpendicular faces (Fig. 1). The rate at which air pressure falls in a bottle of known volume, and pressure slightly above atmospheric, when the bottle discharges through each disc, is

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Herbert Hoover

IT is always a pleasure for me to join in the Ameri-can Mining Congress, for not only has my own professional life been closely linked with the industry, but the Secretary of Commerce is specifically enjoined in the organic act creating the office to promote and foster the interests of the mining industry. And it is a vital part of our national life. It is one of those indus-tries without which. the nation could not go on for a week. It ranks second only to the agricultural industry in its contribution to our raw materials. Its production amounts to nearly 6 ½ billions annually, providing direct support to probably ten millions of our people through employment to about two million workers. But the in-dustry has a greater importance than even these figures indicate, for with agriculture, forestry, and water power it furnishes the raw materials upon which the whole work of our civilization rests. When the raw ma-terials of our mines emerge. from manufacture with the added expenditure of labor and capital upon them, they have a wholesale value of over fifteen billions of dollars. And in this, the second stage of their application, they give employment to another two million workers and support to about ten million more of our people. A large portion of these manufactured commodities must filter through the retail trade; their total value when delivered to the consumer exceeds twenty billions of dollars. And from this distribution arises the support of many more millions of our people. It is estimated that the products of agriculture when they reach . the consumer, with transportation, manu-facturing, and distribution costs added, have about the same value as the mineral industries-each of them thus contributing about one-quarter of our total na-tional income. No other continent has demonstrated its possession of such a magnitude of minerals as has ours, and such a bountiful distribution over our whole land. But our mineral resources differ in one essential from our other natural resources-they are not renewable. Agricul-ture, forests, and water power replenish their supplies from season to season. Some people conclude from the non-renewable character of the mineral supply that they must shortly be exhausted. The practical question is ,one of time, and time in these matters needs to be measured in generations, and apprehension of exhaus-tion needs to be tempered with many probabilities in-cluding the advance in technical methods of extraction. In some of our minerals, such as coal, iron, and building materials we can, through a knowledge of their geologi-cal structure and occurrence, make fairly good estimates of our reserves. We. know that they will outlast many generations of Americans. In non-ferrous metals and oil, geology affords us no great basis for an estimate of future supply. We only know of the occurrence of minerals of this type by actual exposure of them, and we can thus make no estimates except upon reserves which have been proved by actual development by the process of mining. To develop them ahead merely for national satisfaction of assured future supply would imply an unbearable waste of capital. The consequence is that in these groups there is never a demonstrable assurance of more than a few years' supply ahead of us. Yet we have never failed from year to year to find new deposits and extension of old deposits.

Jan 1, 1928

By D. F. Stoneburner

The thermoelectric power and electrical conductivity of a series of liquid alloys of thallium were determined in order to study the relation of chemical bonding to semiconduction in liquids. The results indicate metallic behavior for the alloys of thallium with arsenic, antimony, and bismuth, while the sulfides, selenides, and tellurides indicate semiconduction. The results are compared with the Properties of the same alloys in the solid state. This work supports the observation that long-range order is not a necessary requirement for semiconduction. PREVIOUS work1,5 has shown that some sulfides and oxides behave as semiconductors in the liquid state. Although the band theory has been of great help in understanding the properties of solid semiconductors, its quantitative application to liquids is difficult. The very existence of liquid electronic semiconductors shows that ascribing the discrete structure of the energy spectrum to strict lattice periodicity, or long-range order, is not always satisfactory. Rather, the short-range order determines the structure of energy levels and the width of the forbidden gap and, consequently, the concentration of free holes and electrons. This is borne out by the analysis of data accumulated by Regel and coworkers.6 The similarity of electronic structure of liquid and solid phases of certain liquid metals was pointed out by Knight et a1.,7 who examined nuclear resonance in solid and liquid Li, Na, Rb, Cs, Mg, Al, Ga, Sn, and Bi. They found noticeable changes in the electronic structure upon melting only in the cases of bismuth and gallium. They concluded that "a liquid metal possesses a band structure which is very like that of the solid, provided the short-range structure is not altered during melting." In semiconductors in which the near-neighbor arrangement remains the same on fusion, the material would be expected to retain its semiconducting properties. The quantum theory of semiconductors, with its band structure of energy levels, is linked exclusively to long-range order. Furthermore, it has limited usefulness in predicting new semiconductors. Many sulfide8-12 have made comparisons of properties on the basis of crystal structure or the position in the periodic table, both methods involving the same factors as chemical bonding. Mooser and Pearson8"10 have pointed out that crystal structure depends on chemical bonding, and that this bonding is a property of the atoms themselves. As the periodic arrangement of the atoms offers an easy comparison of such factors as atomic weight and number of valence electrons it provides clues to expected similarities of bonding for various elements or groups of elements. This approach has led Mooser and Pearson to formulate their valence-bond theory of semiconduction, in which they define a semiconducting bond. These authors state that "semiconductivity is the result of the presence in a solid of predominantly covalent bonds. These lead, through the process of electron sharing, to completely filled s and p orbi-tals in the valence shells of all atoms of elemental semiconductors while in semiconducting compounds only one atom of any two bonded together need acquire closed s and p orbitals. The presence of empty 'metallic' orbitals in some atoms of a compound does not destroy the semiconductivity provided that these atoms are not bonded together; it may, however, give rise to pivoting resonance in

Jan 1, 1965

By F. A. Crossley

The key to disagreements between Blackburn's findings and mine is the word equilibrium". My work attempted to define the equilibrium diagram of the titanium-rich end of the Ti-A1 system. It can readily be shown that Blackburn's conclusions are based primarily on the examination of structures substantially removed from equilibrium. The diagram presented in Fig. 16 is properly labeled a "phase diagram". However, it appears that Blackburn either does not understand or does not accept the difference between "phase diagram" and "equilibrium diagram" as defined in the Metals Handbook.17 The conflict lies not in Blackburn's data but in his interpretation of it, and his use of "transformation", "phase diagram", and "equilibrium diagram" as synonymous terms. I share his view that the light microscope is much inferior to the transmission electron microscope for the study of transformations; but this fact does not render the light microscope useless or untrustworthy. The difficulties experienced with the Ti-A1 system have not been due to the limitations of the light microscope, but rather to the extreme sluggishness in achieving equilibrium at temperatures below 1000° C. Were it not for the light microscope employed with polarized light, the twin phase syndrome' might still be unrecognized and, as a consequence, still adding to the confusion of Ti-A1 investigations. (Ref. 1 should read ... Contract No. N161-25952 ... vol. 236.) Other, more sophisticated techniques, including electron transmission, simply confirm the erroneous tentative conclusions drawn from observations of structures due to the twin-phase syndrome. By the standards of most of the investigations of the Ti-A1 systems, seven of the fifteen compositions investigated by Blackburn were seriously contaminated with oxygen. The writer has found that 0.1 wt pct 0 shifts the a + Ti3A1 boundary to 1 at. pct lower A1 content at 700°C. At constant aluminum content, this corresponds to a temperature shift of the boundary of +25°c.18 Blackburn advises that the first group of alloys contained 0.1 to 0.15 wt pct 0, bur he does say whether the analyses were performed on as-received material or on specimens in their final state of heat treatment. This is especially important considering the 20-mil-thick starting materials. If specimens had been annealed in the two-phase a + 6 region it would have provided an indication of the final degree of oxygen contamination since up to about 12 at. pct A1 the boundaries of this region are well-defined for low-oxygen alloys. Blackburn questions the capability of light microscopy in determining phase boundaries in the Ti-A1 system. I submit that the a/a + Ti3A1 boundary in Fig. 1 of Ref. 1 over the composition range from 10 to 18 at. pct A1 was determined by dilatometry and supported by electron diffraction. Specimens of alloys containing 8, 10, 12, and 14 at. pct A1 were aged at 550°C for 1000 hr (under stress of 5000 psi to accelerate the tendency to equilibrium) and then fractured in tension at room temperature. Collodion was applied to the as-fractured (unetched) surface and, when stripped, carried away particles identified by electron diffraction as Ti3A1. Perhaps Blackburn will explain why these electron diffraction data were ignored. At this time, a technique for revealing or indicating

Jan 1, 1969